A space \(\mathbb {T}_p(J) \subset C^{p}(J)\)  of dimension \(p+1\)  is an ECT-space on \(J\)  if and only if there exist positive functions \(w_{j} \in C^{p-j}(J)\) , \(j=0,1,\ldots , p\)  such that \(\mathbb {T}_p(J)\)  is spanned by the following functions [1]}, [2]}, [3]}:
\({\left\lbrace \begin{array}{ll}g_0(x) w_0(x), \\g_1(x) w_0(x) \int _{z}^x w_1(y_1) {\rm d}y_1, \\\hspace*{31.2982pt} \vdots \\g_p(x) w_0(x) \int _{z}^x w_1(y_1) \int _{z}^{y_1} \cdots \int _{z}^{y_{p-1}} w_p(y_p) {\rm d}y_{p} {\rm d}y_{p-1}\cdots {\rm d}y_1,\end{array}\right.}\) 
